plasma heating and asymmetric reconnection in cmesnamurphy/presentations/murphy_god… · 28/9/2010...

IntroductionPlasma Heating in CMEs

Asymmetric Reconnection in CME current sheetsConclusions and Future Work

Plasma heating and asymmetric reconnection inCMEs

Nick Murphy

Harvard-Smithsonian Center for Astrophysics

September 28, 2010

Collaborators: John Raymond, Kelly Korreck, Carl Sovinec,Paul Cassak, Jun Lin, Chengcai Shen, & Aleida Young

Nick Murphy Plasma heating and asymmetric reconnection in CMEs



OutlineIntroduction

Outline

I Plasma heating rates of the 28 June 2000 CMEI Observations (UVCS, LASCO, EIT, MLSO/MK4, GOES)I Using a time-dependent ionization analysis to constrain heatingI Candidate mechanisms and connections with the laboratory

I Asymmetric reconnection in CME current sheetsI A scaling analysis of asymmetric outflow reconnectionI Simulations of X-line retreatI Deriving an expression for X-line motion




OutlineIntroduction

Introduction

I The understanding of astrophysical phenomena usually beginswith the energy budget

I The kinetic and potential energies of CMEs can be obtainedusing white light coronagraph measurements (e.g., Vourlidaset al. 2000)

I The magnetic field of the corona is difficult to diagnose

I The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHOallows us to study the thermal energy content of CMEs

I We consider the physics behind one heating mechanism indetail: upflow from the CME current sheet




UVCS, LASCO, EIT, MLSO, and GOES observationsUsing a time-dependent ionization code to find heating ratesCandidate heating mechanismsConnections with laboratory plasma experiments

On 28 June 2000, a fast and powerful CME was observedby SOHO/UVCS

I SOHO/EIT 195 A observations show a rising dark arcadebetween 18:00–18:48

I GOES observed a C3.7 class X-ray flare starting at 18:48 UT

I While light coronagraph observations by the Mauna Loa SolarObservatory (MLSO) show possible kinking of the rising fluxrope

I Ciaravella et al. (2005) use UVCS and LASCO measurementsto detect a coronal shock wave driven by this event

I A fast, powerful CME with a weak flare





SOHO/EIT observations show a rising dark arcade at 195A followed by bright He ii arches at 304 A

I From left to right: 195 A at 18:48 UT and 19:13 UT, and 304A at 19:19 UT





SOHO/LASCO observations show the rising prominencecrossing the UVCS slit





We use two independent methods to find UVCS densities

1. The ratio of the [O v] λ1213.9 forbidden line to the O v]λ1218.4 intercombination line (Akmal et al. 2001)

2. Radiative pumping of the O vi λλ1031.9, 1037.61 doublet bychromospheric Ly β, O vi, or C ii emission (Raymond &Ciaravella 2004, Noci et al. 1987)

I The collisional ratio is 2:1, so departures from this are due toradiative pumping

I Provides both density and total velocity information





From LASCO and UVCS observations we identify sixfeatures to analyze

Blob Time log ne Description

A 19:12 7.0 Near leading edgeB 19:14 7.2 Near leading edgeC 19:16 6.7 Between leading edge and prominenceD 19:21 6.6 Between leading edge and prominenceE 19:27 6.6 Between leading edge and prominenceF 20:11 6.6 Prominence





UVCS observations show a diagonal feature in O v andO vi at 20:11 UT (Blob F)

I Observed lines include O v, O vi, Lyα, Ly β, C ii, C iii,N iii





Weak Lyα in Blob F allows both [O v] and O v] to beobserved

I The N iii λλ989, 991 lines sometimes appear at the sameposition on the detector as [O v] at 1213.9 A





We use a 1-D time-dependent ionization code to trackejecta between the flare site and UVCS slit

I We run a grid of models with different initial densities, initialtemperatures, and heating rates (e.g, Akmal et al. 2001)

I The final density is derived from UVCS observations

I Assume homologous expansionI Multiple heating parameterizations

I An exponential wave heating model by Allen et al. (1998)I The expanding flux rope model by Kumar & Rust (1996)I Heating proportional to n or n2

I Velocities are scaled from Maricic et al. (2006)

I The models consistent with UVCS observations give theallowable range of heating rates





Caveats and considerations

I Observations are averaged across the line of sightI UVCS may be observing multiple components at different

temperatures simultaneouslyI We assume that O v and O vi emission is from the same

plasma, and take Lyα, C ii, C iii, and N iii emission as upperlimits

I Some heating parameterizations are not amenable to a 1-Danalysis

I Reconnection outflow from the CME current sheetI Kink-like motions driving waves which then dissipate

I No physical heating mechanism is assumed, except for thewave heating model





Total heating, kinetic energy, and potential energy(keV/proton)

Blob QAAH Q ∝ n Q ∝ n2 QKR K.E. P.E.

A 1.0–3.8 2.3–9.0 — 1.1–29 28 (>6.0) 0.78B 0.03–3.7 2.3–15 186-466 1.7–44 34 (>5.5) 0.82C 0.03–4.0 0.1–15 30–476 0.5–44 28 (>5.6) 0.81D 0.02–2.9 0.06–11 32–511 0.8–48 28 (>4.0) 0.83E 1.4 2.9 545 2.1–4.7 34 (>2.3) 0.86F 1.8–4.4 3.1 — 12 1.4 (>1.1) 0.57

I Lower limits to the kinetic energy are given in parentheses

I Total velocities are estimated using O vi pumping

I Q ∝ n2 provides systematically higher heating rates





Discussion

I The total heating is greater than the kinetic energy in thebest constrained feature (Blob F), which is associated withthe rising prominence

I C iii λ977 is blueshifted off of the UVCS panel for Blobs A–Dbut provides a useful constraint when observed

I Radiative pumping of Blob E may be due to chromosphericO i λλ1027.4, 1028.2 instead of Ly β

I The results of this and previous analyses suggest that CMEmodels should take plasma heating into account





Candidate heating mechanisms include:

I Reconnection outflow from the CME current sheetI Recent theoretical/numerical results suggest that most of the

energy goes up

I Wave heating from photospheric motionsI Landi et al. (2010) show that heating ∼1500 times that of

coronal holes would be needed for the ‘Cartwheel CME’

I The kink instability of the expanding flux ropeI But, Vkink < VCME

I Magnetic dissipation/the tearing instabilityI Thermal conduction/energetic particles from flare

I Unlikely because a C class flare is associated with this event





Connections with laboratory plasma experiments

I Tripathi and Gekelman (2010) model an erupting flux ropeand find that intense magnetosonic waves heat the ambientplasma

I Asymmetric outflow reconnection occurs in spheromakmerging experiments (MRX, SSX, TS-3/4)

I Flux rope experiments are performed at MRX, RSX, LAPD,the Caltech spheromak experiment, and elsewhere




Observations of CME current sheetsDeveloping a model for asymmetric reconnectionResistive MHD simulations of X-line retreatDeriving an expression for X-line retreat

Flux Rope Model of Coronal Mass Ejections

I Many models of CMEs predict a current sheet behind therising flux rope (e.g., Lin & Forbes 2000)





Observations of CME current sheets

I Current sheets behind CMEs have been observed for a numberof events (e.g., Ko et al. 2003; Lin et al. 2005; Ciaravella &Raymond 2008; Savage et al. 2010)

I Outward-moving blobs could be the result of the tearinginstability in the current sheet (e.g., Lin et al. 2007)





Is reconnection in CME current sheets symmetric?

I Sunward outflow impacts a region of high plasma andmagnetic pressure

I Antisunward outflow encounters the rising flux rope

I The upstream magnetic field strength and density are bothstrong functions of height

I Seaton (2008) predicts that the majority of the outflow isdirected upward towards the rising flux rope, and that the flowstagnation point and magnetic field null should be near thebase of the current sheet

I Savage et al. (2010) track upflowing (downflowing) featuresabove (below) h ∼ 0.25R� in the 9 April 2008 ‘Cartwheel’CME current sheet. This is near the X-line in pre-eventmagnetic field models.





Developing a model for asymmetric reconnection

I The above figure represents a long and thin reconnection layerwith asymmetric downstream pressure (Murphy, Cassak, &Sovinec, JGR, 2010). Reconnection is assumed to be steadyin an inertial reference frame.

I ‘n’ denotes the magnetic field null and ‘s’ denotes the flowstagnation point





Finding scaling relations for asymmetric outflow

I From conservation of mass, momentum, and energy we arriveat

2ρinVinL ∼ ρLVLδ + ρRVRδ

ρLV2L + pL ∼ ρRV 2

R + pR

2VinL

(αpin +

B2in

µ0

)∼ VLδ

(αpL +

ρLV2L

2

)+VRδ

(αpR +

ρRV 2R

2

)where α ≡ γ/(γ − 1) and we ignore upstream kineticenergy/downstream kinetic energy and assume thecontribution from tension along the boundary is small or even.





Deriving the outflow velocity and reconnection rate

I In the incompressible limit

V 2L,R ∼

√4

(c2in −

p

ρ

)2

+

(∆p

2ρ

)2

± ∆p

2ρ

using p ≡ pL+pR2 , ∆p ≡ pR − pL, and c2

in =B2

inµ0ρin

+ αpinρin

I By assuming resistive dissipation, the electric field is thengiven by

Ey ∼ Bin

√η (VL + VR)

2µ0L





Implications

I The scaling relations show that the reconnection rate isweakly sensitive to asymmetric downstream pressure

I If one outflow jet is blocked, reconnection will be almost as fastI Reconnection will slow down greatly only if both outflow jets

are blockedI The current sheet responds to asymmetric downstream

pressure by changing its thickness or length

I However, this analysis makes three major assumptions:I The current sheet is stationaryI The current sheet thickness is uniformI Magnetic tension contributes symmetrically along the

boundaries

I To make further progress, we must do numerical simulations





Resistive MHD simulations of X-line retreat

I The 2-D simulations start from a periodic Harris sheet whichis perturbed at two nearby locations (x = ±1)

I The reconnection layers move away from each other as theydevelop (Murphy 2010; see also Oka et al. 2008)

I Domain: −30 ≤ x ≤ 30, −12 ≤ z ≤ 12

I Simulation parameters: η = 10−3, β∞ = 1, S = 103–104,Pm = 1, γ = 5/3, δ0 = 0.1

I Define:I xn is the position of the X-lineI xs is the position of the flow stagnation pointI Vx(xn) is the velocity at the X-lineI dxn

dt is the velocity of the X-line





NIMROD solves the equations of extended MHD using afinite element formulation (Sovinec et al. 2004)

I In dimensionless form, the equations used for thesesimulations are

∂B

∂t= −∇× (ηJ− V × B) + κdivb∇∇ · B (1)

J = ∇× B (2)

∇ · B = 0 (3)

ρ

(∂V

∂t+ V · ∇V

)= J× B−∇p −∇ · ρν∇V (4)

∂ρ

∂t+∇ · (ρV) = ∇ · D∇ρ (5)

ρ

γ − 1

(∂T

∂t+ V · ∇T

)= −p

2∇ · V −∇ · q + Q (6)





The current sheets have characteristic single wedge shapes





The outflow away from the obstruction is much faster

I In agreement with Seaton (2008) and Reeves et al. (2010),most of the energy goes away from the obstructed exit





The flow stagnation point and X-line are not colocated

I Surprisingly, the relative positions of the X-line and flowstagnation point switch

I This occurs so that the stagnation point will be located nearwhere the tension and pressure forces cancel





Late in time, the X-line diffuses against strong plasma flow

I The stagnation point retreats more quickly than the X-line

I Any difference between dxndt and Vx(xn) is due to diffusion

I The velocity at the X-line is not the velocity of the X-line





Deriving an expression for X-line retreat

I The inflow (z) component of Faraday’s law for the 2Dsymmetric inflow case is

∂Bz

∂t= −∂Ey

∂x(7)

I The convective derivative of Bz at the X-line taken at thevelocity of X-line retreat, dxn/dt, is

∂Bz

∂t

∣∣∣∣xn

+dxn

dt

∂Bz

∂x

∣∣∣∣xn

= 0 (8)





Deriving an expression for X-line retreat

I From Eqs. 7 and 8:

dxn

dt=

∂Ey/∂x

∂Bz/∂x

∣∣∣∣xn

(9)

I Using E + V × B = ηJ, we arrive at

dxn

dt= Vx(xn)− η

[∂2Bz∂x2 + ∂2Bz

∂z2

∂Bz∂x

]xn

(10)

I In resistive MHD, usually ∂2Bz∂z2 � ∂2Bz

∂x2

I This corresponds to diffusion of the normal component of themagnetic field along the inflow direction





Mechanism and implications

I The X-line moves in the direction of increasing reconnectionelectric field strength

I X-line retreat occurs through a combination of advection bybulk plasma flow and diffusion of the normal component ofthe magnetic field

I X-line motion depends intrinsically on local parametersevaluated at the X-line





Simulations of multiple X-line reconnection

I NIMROD simulations with multiple initial perturbations wereanalyzed by A. Young

I Isolated or strong perturbations are more likely to surviveI Winning X-lines early on have plasma pressure facilitating

outflow rather than impeding itI When an X-line is located near one end of the current sheet,

the flow stagnation point is located in between the X-line anda central plasma pressure maximum

I The number of X-lines changes due to diffusion of the normalcomponent of the magnetic field

I SHASTA simulations by C. C. Shen and J. Lin show that thedirection of plasmoid ejection is related to the relativelocations of the flow stagnation point and X-line

I If xs > xn, then Vplasmoid > 0




ConclusionsOpen questionsFuture work

Conclusions

I CME heating occurs even after the ejecta leaves the flare siteI The total heating is comparable to or greater than the kinetic

energy of the ejectaI Models of CMEs should evolve the energy equation

I Several candidate mechanisms can be ruled out for the 28June 2000 CME because there is insufficient energy in theflare to heat the ejecta

I Thermal conduction, energetic particles from flare region

I Asymmetric reconnection in CME current sheets probablycauses most of the energy and mass to go upward

I X-line retreat occurs due to a combination of advection by thebulk plasma flow and diffusion of Bz





Open questions

I What mechanism(s) are responsible for heating of CMEs?

I Do flareless CMEs show less heating than CMEs with powerfulflares?

I Do fast CMEs show more heating than slow CMEs?

I What is the role of the CME current sheet in the mass andenergy budget of CMEs?

I Where are the X-line and flow stagnation line located in CMEcurrent sheets?

I What are the roles of the plasmoid and tearing instabilities inCME current sheets?





Future work

I To answer the questions on the previous slide, we need toinvestigate multiple events using a standardized method ofanalysis

I Therefore, we will perform our time-dependent heating analysisfor ∼10–20 CMEs

I This will allow us to investigate how heating depends onlocation, CME properties, and other parameters

I We will extend simulations of X-line retreat to include3-D/two-fluid effects

I Applicable to the magnetospheric and turbulent reconnection


plasma heating and asymmetric reconnection in cmesnamurphy/presentations/murphy_god… · 28/9/2010...

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